A ten thousand year ko, thousand year ko or mannenko is a ko that is not interesting for either Black or White to start early on. Players usually wait until very late [1] in the game to actually start it. One of the players also has the option of turning it into a seki.
A basic corner shape that leads to this mannenko is the long L group. The source of this ko is shown below [2].
Bill Spight: It is difficult for either player to start a ten thousand year ko because, when the ko is converted to a regular ko, the other player takes first.
It is easier for Black to convert this ko because Black has less at stake.
[1] Dieter: I have difficulty understanding this. In the given position, if White wins the ko White makes 18 points whereas if Black wins it Black makes 10 points, compared to the "neutral state" which is seki. This means (in my humble opinion but I'm not at all sure) that White must maintain a set of bigger ko-threats than Black's. There are three phases in the game. The first one occurs when White's threats are big enough to fight the ko. The last one occurs when Black's threats have become too small to fight the ko. In between there is the phase where White's threats aren't big enough (<18 points) but Black's are (>10 points). Isn't this the phase where the ko will be started by Black ?
Of course, it is a strong assumption that both sets of threats will decrease in value at the same rate.
TDerz Dieter, the evaluation of making some n points by winning (any) ko is much to simplified. Always the value of the ko-threat not replied to must be deducted from that move, sometimes even another sente. I have drafted a calculation of all possible outcomes above, however, I want to have it perfect before putting it onto the net. One key issue is, that it takes a move to toggle between these two positions!
Bill: You also need to factor in the fact that White can make a regular ko right away, while it takes Black 2 plays to do so.
It is possible to work out correct play for every ko threat situation, but that takes a bit of work. :-) If neither player has a ko threat the result is seki. If either player is komaster, however, it is counterintuitive, but the koloser should make the ko early to get what he can in exchange for losing the ko.
Real life is more complicated, as the ko threat situation can change with time, and making and preventing ko threats may be a major factor in the play elsewhere. ;-)
[2] The above example was borrowed from an article by John Fairbairn that appeared on the MSOWorld site
The paragraph which goes with the diagram follows:
Bill: Takahashi seems to have been the only person ever to avail himself of that option, leading to a rules crisis and a strange decision: Segoe won but Takahashi did not lose.
Bildstein: I saw this shape in one of my games. It seems to be a mannenko where it is the player on the inside that has the option of making a seki.
White can make a ko at a, and she will have to make the first ko threat. Black can make a ko at b, and he will have to make the first ko threat. And Black can make a seki at a. Although, even after the seki, he can play b, have three stones captured, recapture to the right of a, and return to the original position.
See throwin ko.